
Follow your vet's advice. My vet vaccinates at 10 weeks and 12 weeks, and the pups are safe to go on the ground a week - 10 days after the second - so yes, 13, nearly 14 weeks old. But of course they are still taken out and about for socialsation in the meantime - they just have to be carried. By the time a lab is 13 weeks old it is a hefty lump to carry (I know, I've done it!) but it's worth it. It helps you develop the strong arms you are going to need when teaching the 'heel'!
And yes, your vet is likely to repeat the parvo part of the vaccine, just to be certain that it's been given.
I would certainly discuss with your vet the advisability of getting your others boosted slightly early - it sounds like a sensible idea, but there may be disadvantages I haven't considered.
Have fun with your pup!
:)